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%I #13 Sep 20 2019 07:31:30
%S 14,15,16,18,20,24,27,38,46,68,87,124,141,152,155,158,161,166,171,183,
%T 185,186,195,203,208,209,212,218,221,222,226,230,231,232,234,247,249,
%U 255,261,272,275,276,290,295,299,301,306,314,322,323,330,335,341,343
%N Becomes prime or 4 after exactly 3 iterations of f(x) = sum of prime factors of x.
%C f(x) = sum of prime factors with multiplicity, so that f(1500) = 2+2+3+5+5+5 = 22.
%H Andrew Howroyd, <a href="/A048125/b048125.txt">Table of n, a(n) for n = 1..10000</a>
%t f[n_] := Total[Times @@@ FactorInteger[n]];
%t okQ[n_] := For[k = 3; r = n, k >= 1, k--, r = f[r]; If[r == 4 || PrimeQ[r], Return[k == 1]]];
%t Select[Range[500], okQ] (* _Jean-François Alcover_, Sep 20 2019, from PARI *)
%o (PARI) sopfr(n)={my(f=factor(n)); sum(i=1, #f~, f[i,1]*f[i,2])}
%o ok(n)={forstep(k=3, 1, -1, n=sopfr(n); if(n==4||isprime(n), return(k==1))); 0}
%o select(ok, [1..500]) \\ _Andrew Howroyd_, Sep 14 2019
%Y Cf. A002217, A048124.
%K nonn
%O 1,1
%A _David W. Wilson_
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